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P. Berck 2
Water Economics
Rain property rights
Reservoirs, Canals, and Treatment Efficient Pricing Border Prices Subsidies for Whom?
P. Berck 3
Property Rights
Limited as to extent right to use: consumptive use v. total use transport: use only here or can transport hydraulic mine: damaging uses
prohibitedWater flow is Stochastic
some years a lot, others a little
P. Berck 4
The Uncertainty Paradigm
Distinct states of nature (SON) rains a little. Say 0 - 10”, 1000 ac ft available medium amount, say 11 - 20”, 2000 ac ft rains a high amount, say 20” +, 4000 ac ft.
Probability of each SON PL + Pm + Ph =1
Rights give rules by SON
P. Berck 5
Two Types of Theoretical Rights
Sharing x% of flow in each
state of nature. IBM& Barley same
cutback in low flow Disk Plant would want
to buy water from Barley farm in 0-10” state.
Not efficient if can’t buy
Contingent Claims Market for water by
state of nature e.g. 1000 ac ft
when rainfall is 0-10” this year
Arrow Debreu show that CE w.r.t. contingent claims is PO
P. Berck 6
Real Types of Rights
Appropriative First in use, first in
right. Must use. May transport. Is quantified
Riparian Live next to river and
can use it to flood land. Use not req.
Not strictly quantified
Contractual Classes of users priority among classes sharing within classes
Reserved High prority, no need
to use
Open Access Take what you want.
P. Berck 7
In California (See Map)
Individual Appropriators
Quasi Gov appropriators
RipariansExchange
ContractorsWater Districts and
their customers
State and Fed Project
Delta-MendotaFriant dam and S.ShastaSan Luis UnitKesterson and
Drain
P. Berck 8
EBMUD
Junior to Woodbridge
Mokelumne is more than 100% appropriated
Dam for 1000/ ac ft?
Fear of Adjudication
Could buy water and have less.
(Fish would get more)
P. Berck 9
Rights Issues
Transferability Within Basin? Between Basins Security of transferred rights Damage to non-participants
Security Use it or lose it.
Availability every two weeks? Little bits daily?
P. Berck 10
Claims about Appropriative Rights
Transferable, Divisible, Appropriative rights are equivalent to contingent claims. By Arrow-Debreu, they are efficient. (Berck and Lipow)
Every utility maximizer prefers senior to junior appropriative rights. (Burness and Quirk)
P. Berck 11
State Contingent Claim
Expand notion of goods to include things like Umbrella when it rains Umbrella when it doesn’t rain
Every state of nature has different goods
CE w.r.t. contingent goods is PO
P. Berck 12
Contingent Claims
Right to water in ONLY one SON is a contingent claim.
Treat each contingent claim as a separate good.
Means can buy and sell “water if there are between 0 and 10” of rainfall”
First Welfare Theorem says a Competitive Equilibrium is a Pareto Optima.
P. Berck 13
Contingent Claim example
1 has purchased 3 different claims 1000 if there is 1000 ac ft available 1500 if there is 2000 ac ft available 1500 if there is 4000 ac ft available
2 has purchased 2 different claims 500 if there is 2000 ac ft available 2500 if there is 4000 ac ft available
Supply = Demand for water in all SON
P. Berck 14
Appropriative Rights
W is water flow and is random 1000, 2000 or 4000 ac
ft
Aj is water right of jth individual 1st: 1500 ac ft 2nd: 2500 ac ft
i < k Ai is water rights of individuals prior to k. A1 = 0
A2 = 1500
(A3, if he existed, = 4000.
P. Berck 15
Appropriative (con’t)
k gets min(ak,Ak) 1 gets: 1000, 1500,
1500 2 gets: 0, 500, 2500 (3 would get 0,0,0)
get the minimum of what’s left or your rights.
ak =
Max(0, W - i < k Ai) a1 = 1000, 2000,
4000 depending on how
much there is. a2 = 0, 500, 2500
is water left over for individuals k when the flow is W
P. Berck 16
Stochastic Dominance 1st degree
Consider rights of equal quantity (e.g. 1500 each)
In every SON the Senior rights holder (1) gets no less than the Junior rights holder 2.
It does not matter what the probabilities of the states are.
Every water-lover would prefer to be senior to being junior.
P. Berck 17
Senior is better
F(W) is CDF of Water Availabilityak= Max(0, W - i < k Ai)
water available to k and junior
Gk(a) = F(i < k Ai +a) for a 0; else 0. CDF of water available to k and junior
Claim: Gk FSD Gk+n
P. Berck 20
Efficiency of ‘Appropriative’
Wi is water in state of nature in states of natureneed n appropriators Ak = Wk- Wk-1
so that all water is claimedBuy kth right and get water in state of
nature k or moreSell k+1th right and get water ONLY in
state k! State Contingent Claim
P. Berck 21
Reality Check
Real systems don’t turn off IBM and grow barley, even if IBM is “junior”
Class I II and III water on the Fed. Project are attempts to capture state contingent nature
Israeli base allocation with high price over base is another method
P. Berck 22
Marginal Revenue Product
MRPw =P (F(K,W+1) - F(K,W)) k is another input, capital or fertilizer w is water P is the price of the ag. output, cotton.
Use an input until its price r, r = MRPw
This is a rule for profit max. Can you prove it?
P. Berck 23
Economic Efficiency
Price = MRP Price is the (marginal) value of what is
produced with the waterWhat price? Border Pricing Rule
Value of tradable is it’s price in trade Gifts from government don’t count in
price Non-tradable goods used to make
tradables can also be priced this way
P. Berck 24
Water Delivery
Rain, Reservoirs, Canals, and Treatment
Should charge Value of Raw Water + Marginal Cost of Storage+ Marginal Cost of Transfer + Marginal Cost of Treatment
P. Berck 25
Price: An Example
Cotton is marginal crop Acreage adjusts to economic conditions. Assume Average Yield 70 cents per lb for cotton 12 c is value of cotton from additional m3
of water.Dinar and Ariel; Calif. ‘91UC Coop Ext cost data only 8 c /m3
Kislev, Israel Av. 1980-88. 8.7 c/m3
P. Berck 26
MC of Transport
Israel/Jordan/West Bank MC is between 2 and 50 c/m3
2 near the Jordan 50 in the Negev (Bank, 1990)
Efficiency: On average, grow less cotton in Negev Grow more crops near Jordan River
P. Berck 27
California Cotton
Power is priced too low. (Border Price) Capital costs are intentionally subsidized
(not MC) Operating costs are misstated on low side
(is MC) Cotton is subsidized (Border Price)
Efficiency? Less field crops in dry times in Westlands
P. Berck 28
P MC
In agriculture, Water often can not pay its transport cost, much less storage or treatment
Underlying value of water (value of rain) is taken as zero.
Underlying value of water needs to be found
P. Berck 29
Value of Water Rights
markets give best evidence of value of underlying rights
CA has limited markets for water rights
markets also lead to efficiency in water allocation
there are many caveats
P. Berck 30
Water Sales are Difficult
Rights weren’t (and in Mid-east aren’t) saleable
Ag. and Urban not same waterDownstream users objectMultiple agencies all end up with veto
suppose every time you tried to buy a candy bar you had to notify your dentist?
P. Berck 31
Water is Scarce?
When the price is set at zeroIn Drought CA bought water at $125/ac-ftCouldn’t sell at $250 and had to dump itCa and Israel: 75%+ of water goes to Ag.
Some of this water actually makes GDP lower A great deal of it is at value less than $125/ac-ft
which is low for industry and drinking
P. Berck 32
Price Water by Wetness
Water when it is a wet year isn’t scarceWater when it is a dry year is scarceNeither Israeli nor Ca. Systems change
price enough when supply changesPossible in both cases to shut down
Semi-conductors and grow wheatDams make wet-year water into dry
year water
P. Berck 33
Water Storage Projects
Build when P of output made with project water greater than Cost, or B/C > 1
Use border prices for region’s marginal output, like cotton for potential imported intermediates,
like alfalfa pellets for energy to pump the water